The radius of a circular ground is 56,m. A 7, | vedclass

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(C) The outer radius of the circular ground is $R = 56\,m$.The width of the road is $7\,m$,so the inner radius is $r = 56 - 7 = 49\,m$.The shaded regi

Vedclass · Accepted Answer

$15400$

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(C) The outer radius of the circular ground is $R = 56\,m$.The width of the road is $7\,m$,so the inner radius is $r = 56 - 7 = 49\,m$.The shaded region is a sector of an annulus with a central angle $	heta = 60^\circ$.The area of the shaded region is given by the formula:Area $= \frac{	heta}{360^\circ} 	imes \pi 	imes (R^2 - r^2)$Area $= \frac{60^\circ}{360^\circ} 	imes \frac{22}{7} 	imes (56^2 - 49^2)$Area $= \frac{1}{6} 	imes \frac{22}{7} 	imes (56 - 49)(56 + 49)$Area $= \frac{1}{6} 	imes \frac{22}{7} 	imes 7 	imes 105$Area $= \frac{1}{6} 	imes 22 	imes 105 = 11 	imes 35 = 385\,m^2$.The cost of repairing is at the rate of ₹ $40/m^2$.Total cost $= 385 	imes 40 = ₹ 15400$.

The radius of a circular ground is $56\,m$. $A$ $7\,m$ wide road runs around its boundary inside the ground. Some region of the road as shown by the shaded part in the diagram is to be repaired. Find the cost of repairing at the rate of ₹ $40/m^2$ (in ₹).

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